Food labels tell you about what is in the food you
eat. The nutrition-facts label lists the percentages of
macronutrients (protein, carbohydrates, and fat) as well
as vitamins and minerals in each serving. However, it
often does not tell you exactly how much of each thing is
in the food or how much you should have each day to be
healthy.
If you know how much Vitamin C is in a serving, can
you figure out how much is needed in a day? To help you answer a question like that, in
this section you will develop strategies for finding information about parts and wholes.
5-1. WHAT ARE YOU EATING?
The government has created guidelines for how much of various nutrients, vitamins, and
minerals a person should eat or drink each day to be healthy. These guidelines are then
used to create labels like the one shown above to inform the public about the nutritional
content of food.
According to the sample label above, one serving of Cheesy Mac macaroni and cheese
contains 15% of the recommended daily amount of saturated fat that a person should
eat. Nutritionists recommend that a person should have no more than a certain amount of
saturated fat each day. One serving of Cheesy Mac has 3 grams (3g) of saturated
fat. How many grams of saturated fat should a person eat in one day?
Your task: With your team, determine how many grams of saturated fat a person should
eat each day. Look for more than one way to solve the problem and be ready to explain
your reasoning.
What information do we have about the part?
What do we know about the whole?
How could we represent this situation with a number line?
5-2. To help you represent the situation in problem 5-1, copy the number line below on
your paper.
A. With your team, decide how to partition the line (divide it
into equal parts) so that 15% is shown. Why did you choose
to make that number of parts? Is there another way that you
could have divided the line?
B. The amount of saturated fat in one serving of Cheesy Mac is
3 grams. Where should 3g be labeled on the number
line? Add this number to your diagram and justifyyour
decision.
C. Use your diagram to help you decide how much saturated fat is in the
recommended daily serving. Record your thinking.
5-3. One way to write a percentage is as a ratio (comparison) of parts out of 100. For
example, the ratio
represents 15 parts out of 100 total parts.
A. Jill represented the amount of saturated fat in the recommended daily amount with
the ratio
. What does the 3 represent? What does the 20 represent?
B. The ratios
and
are two different ways to compare the saturated fat in one
serving to the recommended daily amount. How can you show that the ratios are
equivalent (the same)?
5-4. One granola bar contains 4g of dietary fiber. The label says that 4g is 16% of the
daily recommended amount. Louis decided to draw a diagram like the one below to
understand this situation.

A. Copy the diagram on your paper and add the label for 16%.
B. How many grams of fiber are recommended each day? How can you show this
with equal ratios?
C. What percent of fiber should Louis get from other foods? Why is this percent
equivalent to the ratio
?
D. What other amounts are missing on the diagram? Add labels for all parts,
percents, and the whole.
E. Chris is eating cookies that contain 12g of dietary fiber, which he says is 48% of
the recommended daily amount. How can you use ratios and part (b) above to
check that 12g is equivalent to 48%?
5-5. One large carrot contains approximately 6 mg of Vitamin C. The recommended
daily intake of Vitamin C is 60 mg. Resa wanted to find out what percentage of her daily
Vitamin C she gets from one carrot. She started with a line divided into 10 parts.
A. Why do you think she divided the line segment into 10 parts?
B. Copy the diagram on your paper and fill in the missing labels.
C. The ratio
represents the portion of Vitamin C in one large carrot. Work
with your team to find this ratio in the diagram. Where do you see each
amount? What other ratio could you write that would be equal to this?
D. Use the diagram to help you find and write at least two other ratios on the number
line that are equal to each other.
5-6. Resa was mixing blue and red paint to create purple paint. She created the drawing
below to show the portions of blue paint to red that she used.
A. What does the picture tell you about the paint mixture? What statements can you
make?
B. If you have not stated it yet, what percent of the paint is blue? What percent of
the paint is red? Justify your answer.
5-7. Additional Challenge: Turner Middle School has 110 boys. Fifty-six percent of the
students in the school are girls. How many students go to this school?
A. Create a model like Resa’s from problem 5-5. Label the percentage of girls, the
percentage of boys, and the number of boys on your drawing, as well as 0% and
100%.
B. How many students go to the school? How do you know?
C. How many girls go to the school? Explain your reasoning.
5-8. Additional Challenge: Maria is making paper flowers as decorations for the fall
dance. She has made 40 flowers so far, and she is 16% finished. If she plans to finish
making 70% of the total flowers needed by tonight, how many more will she need to
make by then? Show your work.
Equivalent Ratios
A ratio is a comparison of two quantities by division. A ratio can be written in words, as
a fraction, or with colon notation. Most often in this course, ratios will be written as
fractions or stated in words.
For example, if there are 28 students in a math class and 15 of them are girls, you can
write the ratio of the number of girls to the number of students in the class as:
15 girls to 28 students
15 girls : 28 students
You used a Giant One to write equivalent fractions in Chapter 1. To rewrite any ratio as
an equivalent ratio, write it as a fraction and multiply it by a fraction equal to one. For
example, you can show that the ratio of raisins to peanuts is the same for a larger mixture
using a Giant One like this:
Equivalent fractions (or ratios) can be thought of as families of fractions. There are an
infinite number of fractions that are equivalent to a given fraction. You may want to
review the basis for using a Giant One — the Multiplicative Identity — in the Math
Notes box in Lesson 1.2.5.